Optimisation of feed intake is a major aim of pasture and range management for ruminants and understanding what influences feeding behaviour may play an important role in satisfying this aim. An obstacle to such understanding is the fact that feeding is a two-state variable (eating or not eating, albeit with changes in rate of eating during meals), whereas the likely influencing factors are mostly continuous variables. These include gut-fill, concentrations and rates of utilisation of nutrients and metabolites, and changes in nutrient demand due to growth, reproduction and environment, both climatic and social. Catastrophe theory deals mathematically with situations in which an outcome is discontinuous (e.g. eating or not eating) and influencing variables (‘control’ variables in terms of catastrophe theory) are continuously variable (e.g. physiological and environmental factors affecting feeding). We discuss models of feeding and develop an approach in which the Type 2 catastrophe, illustrated by the bifurcation or cusp diagram, is adapted to use negative feedbacks and capacity to handle food and nutrients as the two controlling factors. Ease of prehension, as expressed by rate of eating, is modelled, as are pauses within, as well as between, meals. Quantification has not yet been attempted and the approach is presented to stimulate new thinking about the modelling and prediction of feeding behaviour and meal dynamics.